Students will understand that the unit circle is a fundamental part of Trigonometry.
Students will know terminology (unit circle) and relationships (between the 6 trigonometric functions and the unit circle.), as well as graphs of the three main trigonometric functions.
Students will be able to make sense of the unit circle, and its relationship to the trigonometric functions.
Maine Learning Results Alignment
Maine Learning Results: Mathematics- C. Geometry
Geometric Figures
Grades 9-Diploma
3. Students understand and use basic ideas of trigonometry.
b. Use trigonometry to solve for missing lengths in right triangles.
Rationale: In order for students to get a strong grasp on the basic ideas of trigonometry, they must be understand, and be able to show, where the six trigonometric functions come from, which is the unit circle.
Assessment
Formative (Assessment for Learning)
*During this lesson students will be learn how the six trigonometric functions are derived. At the start of the lesson students will be given a piece a graph paper with a circle drawn in the center. Throughout the lesson students will be responsible to filling out the chart as necessary. As each section of the lesson progresses, I will float around the room to check that students understand the instructions and are filling out the charts correctly. After the lesson, students will be given some time to finish filling in their diagram of the unit circle, including all six trigonometric functions. Students will be given an opportunity to explain their diagrams to a partner of their choice. They will then use this peer feedback to make any adjustments to their diagrams that they see fit. During this session, I will be floating around the room observing student conversations, and giving feedback when appropriate. This will allow me to ensure that all students have a strong understanding of the way the trig functions are derived, before I move onto the homework assignment.
Summative (Assessment of Learning)
For the final product, students will describe the way in which all six functions are derived, step-by-step. After students have completed the in class graphing activity, they will be allowed to ask any questions they may have before moving on to the next section. Students will now need to write a paragraph detailing the steps needed in order to create a unit circle from scratch. They will start this activity in class, so that they will be able to questions about the assignment. Any work not finished in class will be assigned for homework. Along with their paragraphs, they must also post an entry to their blog giving an overview of the day's events. After posted to the blog, students will receive feedback from their peers via comments on each others' blog entries. After receiving feedback, students will have the opportunity to make changes to their entry due the following class. If the choose to make any changes to their blog, they may gain some additional points to their final grade.
Integration
English- Students will work in partners in order to give feedback on each others' progress. Student will also have to a write a paragraph detailing the steps taken in order to derive the six trig functions from the unit circle.
Art- Students will need to create a representation of the unit circle as part of an in-class activity.
Technology- Students will be able to reference the hook while creating their unit circle diagrams.
Groupings
After students have created their unit circle diagrams, they will be given the opportunity to pair up with a partner of their choice. Each student will then takes turns practicing describing the ways in which the trigonometric functions are derived from the unit circle. After this activity, students will then be able to begin constructing their own paragraphs, which are due next class.
Differentiated Instruction
Strategies Logical- Students will be uncovering relationships between unit circle and 6 trigonometric functions. Musical-Background music is playing while students do in class work. Intrapersonal- Students do most of the work independently during the lecture. Interpersonal- Students will compare sketches with one parter of their choice. Bodily-Kinesthetic- Students are sketching out the unit circle, with the freedom to walk around the room for any type of supplies they might need (more graph paper, colored pencils, etc). Verbal- Students will partake in class discussion about the unit circle. Spatial- Sketches and Applets will allow visual learners to see exactly where the trigonometric functions are derived from.
Modifications/Accommodations
I will review student's IEP, 504, or ELLIDEP and make appropriate modifications and accommodations. Absent students are responsible for coming to see me during the next day that they are in class in order to receive any make-up work. Upon meeting with me I will decide, based upon any activities they missed, whether or not they must stay and make up time after school, or if an alternate assignment would be just as sufficient. Absent students have 3 days upon returning to school in order to make up missed work, or, under extenuating circumstances, to make arrangements with me as to when this work will be due. Absent students will lose points for classroom participation, but will be given the option of doing an alternate assignment of my choice in order to make up the lost points.
Extensions
Students will begin the lesson by viewing 2 different versions of completed unit circles. The lesson will focus on deriving the six trigonometric functions from the unit circle, and student will be required to fill out a diagram of the unit circle during the lecture. At several points throughout the lesson I will float around the room, ensuring that all students are able to draw the unit circle accurately. After all students have completed this activity, they will pick a partner of their choice. As each student takes turns explaining the unit circle to their partner, I will float around the room, observing student conversations. In this way, students will be given plenty of opportunity to receive feedback and improve their work.
Materials, Resources and Technology
Graph paper
Protractors
Pens/Pencils
Colored Pencils
Rulers
Laptops
Internet Access
CD of Music to Play in Background
They will also write a paragraph on the class blog describing what they did in class today. They will be able to do this in class if they finish early, otherwise it will be for homework. www.blogger.com
Maine Standards for Initial Teacher Certification and Rationale
Standard 3 - Demonstrates a knowledge of the diverse ways in which students learn and develop by providing learning opportunities that support their intellectual, physical, emotional, social, and cultural development. Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by providing several learning opportunities that speak to different learning styles. By creating a lesson plan that takes different learning styles into account, it creates a more positive and comfortable atmosphere for all students. Several ways this lesson reflects different learning styles is by putting the daily agenda on the board, having a detailed list of instructions, allowing for peer feedback, and by brainstorming ideas. These methods reflect all four learning styles, allowing students with strengths in any given area to benefit from the lesson.
Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory. Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by creating an environment where students must use higher level thinking. Students will explain how the six trigonometric functions are derived from the unit circle. They will also need to interpret different versions of the unit circle (hook). During the in-class activity, students will apply their knowledge of the unit circle in order to create a unit circle of their own. After they have completed their diagrams of the unit circle, they will share their diagram with a partner. Each student will take turns describing their unit circle diagrams to their partners. This will allow them to see a different perspective, as their peers give them feedback on their diagrams. Students will show empathy by understanding each others' perspectives of the unit circle. Students' self-knowledge will also be demonstrated as they reflect upon their peer feedback and makes changes to their diagrams.
Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs. Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by incorporating a variety of methods designed to speak to multiple intelligences in the classroom. Providing an opportunity for several intelligences in a classroom environment ensures that more students will be given a chance to show their strength and provide a better learning environment overall.
Logical- Students will be uncovering relationships between unit circle and 6 trig functions. Musical-Background music is playing while students do in class work. Intrapersonal- Students do most of the work independently during lecture. Interpersonal- Students compare sketch with one parter of their choice. Bodily-Kinesthetic- Students are sketching out unit circle, with the freedom to walk around the room for any typr of supply they might need (more graph paper, colored pencils, etc). Verbal- Will be having class discussion Spatial- Sketches and Applets will allow visual learners to see exactly where the trigonometric functions derive from.
For each class period, students will post blog entry reflecting that days assignment. Peers will then be able to go onto the class blog to provide peer feedback to the student. If the student so chooses, they will be able to update the assignment before the next class period based in the peer feedback they received. The blog will include a post for each lesson, as well as their final assessment. Additional blogs maybe assigned at my discretion.
Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner. Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by providing students with several opportunities for feedback. Students will begin the period by looking at two different versions of the unit circle. Then I will introduce the unit circle and, as I describe it on the board, students will be required to put their own unit circle diagram together at their seats using a piece graph paper with a pre-drawn circle. While students are working, I will be floating around the room, providing feedback when necessary. After students have completed their unit circle diagrams, they will choose a partner to work with. After taking turns describing their unit circle diagrams to one-another, they will receive feedback from their partner. After all students have had a chance to reflect on their feedback, make any changes to their diagrams, or ask any questions they may have, I will move on to the homework. Students' homework will be in two parts; they will write a paragraph, which they will start in class, describing how a unit circle is derived. They need to describe all six functions briefly. Also, students will have to submit a brief blog entry describing the day's lessons. For an example of this, please see attached sample blog entries.
Teaching and Learning Sequence:
The desks will be arranged in a typical classroom set-up, facing the board. Students will be doing a lot of individual work, and this is the best way to let the students have their space, while still allowing them to move chairs around to discuss their diagrams with a partner of their choice, when it comes to that part of the lesson. Students will have the opportunity to take out a laptop and view the applets (hooks) at their seats in order to get an interactive feel of the unit circle. If there is time at the end of class, students will be allowed to take out a laptop and post their work to their blog.
Agenda
Hook students with interactive applets (10 minutes)
In-class unit circle lecture and activity (20 minutes)
Students receive feedback on diagram from partners (10 minutes)
Students make changes/ask questions (5 minutes)
Paragraph describing process started in class (10 minutes)
Any work not done is homework due next class
Students given 5 minute warning before end of class to pack up, and are reminded to write blog entry describing day's events.
Students will be introduced to how trigonometric functions are derived, and where they come from. In class, students will create a diagram of the unit circle as they follow the lecture/discussion. As a summative assessment to show their understanding of the concept, students will be asked to write a paragraph describing how to derive the essential trig functions from the unit circle. This helps students to see the basis behind trigonometry, and as they move forward through more advanced math classes, the unit circle will become an integral part of their lessons. As a hook, students will few the two applets linked in the Sources section on the lesson plan. Both are interactive and give students immediate exposure to the material, as well as a source to refer to while building their own unit circle diagrams in class. This lesson also speaks to a variety of student intelligences as I have mentioned earlier in the lesson plan [See rationale statement for standard 5]. Providing an opportunity for students to express their strengths throughout the their multiple intelligences allows for a greater learning experiences for all students.
Students will know terminology (unit circle) and relationships (between the 6 trigonometric functions and the unit circle.), as well as graphs of the three main trigonometric functions. At the start of the lesson, using the hook, I will define the unit circle for the students. During the lecture, the students will gain an understanding of how the trigonometric functions are related to and derived from the unit circle. I will also briefly introduce them to the graphs of three trig functions, which will be covered more in depth in a later lesson. Throughout the lesson, students will be asked to create a unit circle diagram of their own. At key points in the lesson, I will circle around the room to ensure that all students have a clear understanding of the content, and are filling out the unit circle correctly. After their diagrams have been completed, they will also receive peer feedback, and will be able to answer any additional questions they have before moving on to the homework. For homework, students will need to write a paragraph describing how the trig functions are derived from the unit circle. They will begin this lesson in class, due next class. Also they must write a blog entry, posted by next class, that describes what happened in today's class. For a detailed description of the content, see teacher notes.
Students will be able to make sense of the unit circle, and its relationship to the trigonometric functions. Students will use a piece of graph paper, given to them at the start of the class with an empty circle drawn into it. Students will use this graph throughout the lesson to explore ways to draw the unit circle. While students are working, they will experience music playing in the background. This gives another opportunity for students of various intelligences to show their strengths. As described earlier, throughout the lesson, students will progress through all stages of higher learning. Students will explain how the six trigonometric functions are derived from the unit circle. They will also need to interpret different versions of the unit circle (hook). During the in-class activity, students will apply their knowledge of the unit circle in order to create a unit circle of their own. After they have completed their diagrams of the unit circle, they will share their diagram with a partner. Each student will take turns describing their unit circle diagrams to their partners. This will allow them to see a different perspective, as their peers give them feedback on their diagrams. Students will show empathy by understanding each others' perspectives of the unit circle. Students' self-knowledge will also be demonstrated as they reflect upon their peer feedback and makes changes to their diagrams. To facilitate the learning process, students will be given an empty sheet of graph paper to record their thoughts, as well as a laptop to view the hook shown at the beginning of class, so that they can manipulate it freely. After students have finished creating their unit circle diagrams, they will be allowed to work with a partner of their choice. Each student will give constructive feedback on their partners diagram. Describing their diagrams out loud allows students to rehearse their thoughts. Also, it allows them to rethink any choices they made while they were creating the diagram because they now have to justify their answers. After they have been given peer feedback, students will be allowed to revise their diagram in any way that they see fit. At the end of the activity students will refine their diagrams before handing them in. Once students have a strong grasp of the unit circle, they will be given the opportunity to start their homework in class. For homework, students will write a paragraph describing the steps they took to derive the six trigonometric functions from the unit circle. Also, they are then required to post an entry of the day's events to their blog, due by the start of next class. There is a sample blog attached.
Students will be given several opportunities to self-asses their work. Students will receive peer feedback before handing in a final copy of their unit circle diagrams. Upon receiving feedback, students will be given a final opportunity to make any adjustment to their work before handing in a finished product. Students are also required to submit a blog entry detailing each day's events. Students are to have all blog entries posted by the start of the next class, and I will leave a comment for the student by the end of that day. All homework assignments will be returned to the student with feedback within one week, usually by the next class period. In order for students to gain a strong understanding of trigonometry they need to understand how the functions are derived, where they come from. The unit circle is an essential part of higher level math classes, including Calculus 1. Next class students will be applying the trigonometric functions to problem solving. This series of lessons will build onto one another up to the final performance task as the end of the unit.
UMF LESSON PLAN FORMAT
Teacher’s Name: Ms. Jess L Mitchell Lesson # : 2
Grade Level: 9-12 Topic: Trigonometry
Objectives:
Maine Learning Results Alignment
Geometric Figures
Grades 9-Diploma
3. Students understand and use basic ideas of trigonometry.
b. Use trigonometry to solve for missing lengths in right triangles.
Rationale: In order for students to get a strong grasp on the basic ideas of trigonometry, they must be understand, and be able to show, where the six trigonometric functions come from, which is the unit circle.
Assessment
*During this lesson students will be learn how the six trigonometric functions are derived. At the start of the lesson students will be given a piece a graph paper with a circle drawn in the center. Throughout the lesson students will be responsible to filling out the chart as necessary. As each section of the lesson progresses, I will float around the room to check that students understand the instructions and are filling out the charts correctly. After the lesson, students will be given some time to finish filling in their diagram of the unit circle, including all six trigonometric functions. Students will be given an opportunity to explain their diagrams to a partner of their choice. They will then use this peer feedback to make any adjustments to their diagrams that they see fit. During this session, I will be floating around the room observing student conversations, and giving feedback when appropriate. This will allow me to ensure that all students have a strong understanding of the way the trig functions are derived, before I move onto the homework assignment.
For the final product, students will describe the way in which all six functions are derived, step-by-step. After students have completed the in class graphing activity, they will be allowed to ask any questions they may have before moving on to the next section. Students will now need to write a paragraph detailing the steps needed in order to create a unit circle from scratch. They will start this activity in class, so that they will be able to questions about the assignment. Any work not finished in class will be assigned for homework. Along with their paragraphs, they must also post an entry to their blog giving an overview of the day's events. After posted to the blog, students will receive feedback from their peers via comments on each others' blog entries. After receiving feedback, students will have the opportunity to make changes to their entry due the following class. If the choose to make any changes to their blog, they may gain some additional points to their final grade.
Integration
Art- Students will need to create a representation of the unit circle as part of an in-class activity.
Technology- Students will be able to reference the hook while creating their unit circle diagrams.
Groupings
Differentiated Instruction
Logical- Students will be uncovering relationships between unit circle and 6 trigonometric functions.
Musical-Background music is playing while students do in class work.
Intrapersonal- Students do most of the work independently during the lecture.
Interpersonal- Students will compare sketches with one parter of their choice.
Bodily-Kinesthetic- Students are sketching out the unit circle, with the freedom to walk around the room for any type of supplies they might need (more graph paper, colored pencils, etc).
Verbal- Students will partake in class discussion about the unit circle.
Spatial- Sketches and Applets will allow visual learners to see exactly where the trigonometric functions are derived from.
I will review student's IEP, 504, or ELLIDEP and make appropriate modifications and accommodations. Absent students are responsible for coming to see me during the next day that they are in class in order to receive any make-up work. Upon meeting with me I will decide, based upon any activities they missed, whether or not they must stay and make up time after school, or if an alternate assignment would be just as sufficient. Absent students have 3 days upon returning to school in order to make up missed work, or, under extenuating circumstances, to make arrangements with me as to when this work will be due. Absent students will lose points for classroom participation, but will be given the option of doing an alternate assignment of my choice in order to make up the lost points.
Students will begin the lesson by viewing 2 different versions of completed unit circles. The lesson will focus on deriving the six trigonometric functions from the unit circle, and student will be required to fill out a diagram of the unit circle during the lecture. At several points throughout the lesson I will float around the room, ensuring that all students are able to draw the unit circle accurately. After all students have completed this activity, they will pick a partner of their choice. As each student takes turns explaining the unit circle to their partner, I will float around the room, observing student conversations. In this way, students will be given plenty of opportunity to receive feedback and improve their work.
Materials, Resources and Technology
Protractors
Pens/Pencils
Colored Pencils
Rulers
Laptops
Internet Access
CD of Music to Play in Background
Source for Lesson Plan and Research
http://www.analyzemath.com/unitcircle/unitcircle.html
This website is an alternate view of the unit circle showing all six functions in a fixed location.
http://www.ies.co.jp/math/products/trig/applets/sixtrigfn/sixtrigfn.html
They will also write a paragraph on the class blog describing what they did in class today. They will be able to do this in class if they finish early, otherwise it will be for homework.
www.blogger.com
Maine Standards for Initial Teacher Certification and Rationale
Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by providing several learning opportunities that speak to different learning styles. By creating a lesson plan that takes different learning styles into account, it creates a more positive and comfortable atmosphere for all students. Several ways this lesson reflects different learning styles is by putting the daily agenda on the board, having a detailed list of instructions, allowing for peer feedback, and by brainstorming ideas. These methods reflect all four learning styles, allowing students with strengths in any given area to benefit from the lesson.
Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by creating an environment where students must use higher level thinking. Students will explain how the six trigonometric functions are derived from the unit circle. They will also need to interpret different versions of the unit circle (hook). During the in-class activity, students will apply their knowledge of the unit circle in order to create a unit circle of their own. After they have completed their diagrams of the unit circle, they will share their diagram with a partner. Each student will take turns describing their unit circle diagrams to their partners. This will allow them to see a different perspective, as their peers give them feedback on their diagrams. Students will show empathy by understanding each others' perspectives of the unit circle. Students' self-knowledge will also be demonstrated as they reflect upon their peer feedback and makes changes to their diagrams.
Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by incorporating a variety of methods designed to speak to multiple intelligences in the classroom. Providing an opportunity for several intelligences in a classroom environment ensures that more students will be given a chance to show their strength and provide a better learning environment overall.
Logical- Students will be uncovering relationships between unit circle and 6 trig functions.
Musical-Background music is playing while students do in class work.
Intrapersonal- Students do most of the work independently during lecture.
Interpersonal- Students compare sketch with one parter of their choice.
Bodily-Kinesthetic- Students are sketching out unit circle, with the freedom to walk around the room for any typr of supply they might need (more graph paper, colored pencils, etc).
Verbal- Will be having class discussion
Spatial- Sketches and Applets will allow visual learners to see exactly where the trigonometric functions derive from.
For each class period, students will post blog entry reflecting that days assignment. Peers will then be able to go onto the class blog to provide peer feedback to the student. If the student so chooses, they will be able to update the assignment before the next class period based in the peer feedback they received. The blog will include a post for each lesson, as well as their final assessment. Additional blogs maybe assigned at my discretion.
Rationale: This lesson addresses the Maine Standards for Initial Teacher Certification by providing students with several opportunities for feedback. Students will begin the period by looking at two different versions of the unit circle. Then I will introduce the unit circle and, as I describe it on the board, students will be required to put their own unit circle diagram together at their seats using a piece graph paper with a pre-drawn circle. While students are working, I will be floating around the room, providing feedback when necessary. After students have completed their unit circle diagrams, they will choose a partner to work with. After taking turns describing their unit circle diagrams to one-another, they will receive feedback from their partner. After all students have had a chance to reflect on their feedback, make any changes to their diagrams, or ask any questions they may have, I will move on to the homework. Students' homework will be in two parts; they will write a paragraph, which they will start in class, describing how a unit circle is derived. They need to describe all six functions briefly. Also, students will have to submit a brief blog entry describing the day's lessons. For an example of this, please see attached sample blog entries.
Teaching and Learning Sequence:
Agenda
Students will be introduced to how trigonometric functions are derived, and where they come from. In class, students will create a diagram of the unit circle as they follow the lecture/discussion. As a summative assessment to show their understanding of the concept, students will be asked to write a paragraph describing how to derive the essential trig functions from the unit circle. This helps students to see the basis behind trigonometry, and as they move forward through more advanced math classes, the unit circle will become an integral part of their lessons. As a hook, students will few the two applets linked in the Sources section on the lesson plan. Both are interactive and give students immediate exposure to the material, as well as a source to refer to while building their own unit circle diagrams in class. This lesson also speaks to a variety of student intelligences as I have mentioned earlier in the lesson plan [See rationale statement for standard 5]. Providing an opportunity for students to express their strengths throughout the their multiple intelligences allows for a greater learning experiences for all students.
What, Where, Why, Hook, Tailor: Logical, Musical, Interpersonal, Intrapersonal, Bodily-Kinesthetic, Verbal, Spatial
Equip, Tailor: Logical, Musical, Interpersonal, Intrapersonal, Bodily-Kinesthetic, Verbal, Spatial
Explore, Experience, Rethink, Revise, Rehearse, Refine, Tailor: Logical, Musical, Interpersonal, Intrapersonal, Bodily-Kinesthetic, Verbal, Spatial
Evaluate, Refine, Tailor: Logical, Musical, Interpersonal, Intrapersonal, Bodily-Kinesthetic, Verbal, Spatial